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The composite nature of a shallow bound state is studied by using theweak-binding relation, which connects the compositeness of the bound state withobservables. We first show that the previous weak-binding relation cannot beapplied to the system with a large effective range. To overcome thisdifficulty, we introduce the finite-range correction by redefining the typicallength scale in the weak-binding relation. A method to estimate the uncertaintyof the compositeness is proposed. It is numerically demonstrated that the rangecorrection enlarges the applicable region of the weak-binding relation.Finally, we apply the improved weak-binding relation to the actual hadrons,nuclei, and atomic systems [deuteron, $X(3872)$, $D^{*}_{s0}(2317)$,$D_{s1}(2460)$, $N\Omega$ dibaryon, $\Omega\Omega$ dibaryon,${}^{3}_{\Lambda}{\rm H}$, and ${}^{4}{\rm He}$ dimer] to discuss theirinternal structure from the compositeness. We present a reasonable estimationof the compositeness of the deuteron by properly taking into account theuncertainty. The results of $X(3872)$ and the $N\Omega$ dibaryon show that therange correction is important to estimate the compositeness of physical states.

Structure of exotic hadrons by a weak-binding relation with finite-range correction